- New
-
Topics
- All Categories
- Metaphysics and Epistemology
- Value Theory
- Science, Logic, and Mathematics
- Science, Logic, and Mathematics
- Logic and Philosophy of Logic
- Philosophy of Biology
- Philosophy of Cognitive Science
- Philosophy of Computing and Information
- Philosophy of Mathematics
- Philosophy of Physical Science
- Philosophy of Social Science
- Philosophy of Probability
- General Philosophy of Science
- Philosophy of Science, Misc
- History of Western Philosophy
- Philosophical Traditions
- Philosophy, Misc
- Other Academic Areas
- Journals
- Submit material
- More
Choice principles in local mantles
Mathematical Logic Quarterly 68 (3):264-278 (2022)
Abstract
Assume. Let κ be a cardinal. A ‐ground is a transitive proper class W modelling such that V is a generic extension of W via a forcing of cardinality. The κ‐mantle is the intersection of all ‐grounds. We prove that certain partial choice principles in are the consequence of κ being inaccessible/weakly compact, and some other related facts.My notes
Similar books and articles
Adding a Nonreflecting Weakly Compact Set.Brent Cody - 2019 - Notre Dame Journal of Formal Logic 60 (3):503-521.
Universal partial indestructibility and strong compactness.Arthur W. Apter - 2005 - Mathematical Logic Quarterly 51 (5):524-531.
Strongly unfoldable cardinals made indestructible.Thomas A. Johnstone - 2008 - Journal of Symbolic Logic 73 (4):1215-1248.
Mad families, forcing and the Suslin Hypothesis.Miloš S. Kurilić - 2005 - Archive for Mathematical Logic 44 (4):499-512.
Strongly unfoldable, splitting and bounding.Ömer Faruk Bağ & Vera Fischer - 2023 - Mathematical Logic Quarterly 69 (1):7-14.
Indestructibility and stationary reflection.Arthur W. Apter - 2009 - Mathematical Logic Quarterly 55 (3):228-236.
Choice Principles and Compactness Conditions.Bernhard Banaschewski - 1998 - Mathematical Logic Quarterly 44 (3):427-430.
Inner models with large cardinal features usually obtained by forcing.Arthur W. Apter, Victoria Gitman & Joel David Hamkins - 2012 - Archive for Mathematical Logic 51 (3-4):257-283.
Chain conditions of products, and weakly compact cardinals.Assaf Rinot - 2014 - Bulletin of Symbolic Logic 20 (3):293-314,.
Analytics
Added to PP
2022-05-09
Downloads
11 (#351,772)
6 months
6 (#1,472,471)
2022-05-09
Downloads
11 (#351,772)
6 months
6 (#1,472,471)
Historical graph of downloads
References found in this work
Set-theoretic geology.Gunter Fuchs, Joel David Hamkins & Jonas Reitz - 2015 - Annals of Pure and Applied Logic 166 (4):464-501.
The downward directed grounds hypothesis and very large cardinals.Toshimichi Usuba - 2017 - Journal of Mathematical Logic 17 (2):1750009.
Certain very large cardinals are not created in small forcing extensions.Richard Laver - 2007 - Annals of Pure and Applied Logic 149 (1-3):1-6.
Superstrong and other large cardinals are never Laver indestructible.Joan Bagaria, Joel David Hamkins, Konstantinos Tsaprounis & Toshimichi Usuba - 2016 - Archive for Mathematical Logic 55 (1-2):19-35.
PhilPapers logo by Andrea Andrews and Meghan Driscoll.
This site uses cookies and Google Analytics (see our terms & conditions for details regarding the privacy implications). Use of this site is subject to terms & conditions.
All rights reserved by The PhilPapers Foundation
Server: philpapers-web-68866f4b87-dxklk uwo